An enriched finite element/level-set model for two-phase electrohydrodynamic simulations

In this work, a numerical model for the simulation of two-phase electrohydrodynamic (EHD) problems is proposed. It is characterized by a physically consistent treatment of surface tension as well as a jump in the electric material properties. The formulation is based on a finite element method enriched with special shape functions, capable of accurate capturing discontinuities both in the fluid pressure and the gradient of the electric potential. Phase interface is, thus, represented as a zero-thickness boundary. The proposed methodology allows modeling the electric force as an interfacial one, strictly abiding with the physics. The approach is tested using the droplet deformation benchmarks. Moreover, application of the method to study a three-dimensional (3D) case, not characterized by symmetry of revolution, is shown. The proposed methodology defines a basis for an enriched finite element method for a wide range of EHD problems.